Local weak solution for a multivalued evalution equation

We prove that the Cauchy problem u'(t) ∈ Bu(t) and u(0) = x, in a Banach space, has a local weak solution when B is the sum of the generator of a linear and compact C₀ C semi-group and a conveωiu-usco set-valued mapping. We also include an application of this perturbation result to a semi-linear parabolic equation whose nonlinear term is discontinuous.